Simulations Of Neutron Star Mergers Research Articles

New equation of state for astrophysical simulations

We generate a new complete equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions ready for use in astrophysical simulations of supernovae and neutron star mergers. Our previous two papers tabulated the EOS at over 180,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_P$ = 0 to 0.56. In this paper we combine these data points using a suitable interpolation scheme to generate a single equation of state table on a finer grid. This table is thermodynamically consistent and conserves entropy during adiabatic compression tests. We present various thermodynamic quantities and the composition of matter in the new EOS, along with several comparisons with existing EOS tables. Our equation of state table is available for download.

Testing approximations of thermal effects in neutron star merger simulations

We perform three-dimensional relativistic hydrodynamical calculations of neutron star mergers to assess the reliability of an approximate treatment of thermal effects in such simulations by combining an ideal-gas component with zero-temperature, microphysical equations of state. To this end we compare the results of simulations that make this approximation to the outcome of models with a consistent treatment of thermal effects in the equation of state. In particular we focus on the implications for observable consequences of merger events like the gravitational-wave signal. It is found that the characteristic gravitational-wave oscillation frequencies of the postmerger remnant differ by about 50 to 250 Hz (corresponding to frequency shifts of 2 to 8 percent) depending on the equation of state and the choice of the characteristic index of the ideal-gas component. In addition, the delay time to black hole collapse of the merger remnant as well as the amount of matter remaining outside the black hole after its formation are sensitive to the description of thermal effects.

Equation of state of nuclear matter in a virial expansion of nucleons and nuclei

We study the equation of state (EOS) of nuclear matter at subnuclear density in a Virial expansion for a nonideal gas. The gas consists of neutrons, protons, alpha particles, and 8980 species of nuclei with $A \ge 12$ and masses from the finite-range droplet model (FRDM). At very low density, the Virial expansion reduces to nuclear statistical equilibrium. At higher density, the Virial results match smoothly to the relativistic mean field results discussed in our previous paper. We tabulate the resulting EOS at over 73,000 grid points in the temperature range $T$ = 0.158 to 15.8 MeV, the density range $n_B$ = 10$^{-8}$ to 0.1 fm$^{-3}$, and the proton fraction range $Y_P$ = 0.05 to 0.56. In the future we plan to match these low density results to our earlier high density mean field results, and generate a full EOS table for use in supernova and neutron star merger simulations. This Virial EOS is exact in the low density limit.

Equation of state of dense matter from a density dependent relativistic mean field model

We calculate the equation of state (EoS) of dense matter, using a relativistic mean field (RMF) model with a density dependent coupling that is a slightly modified form of the original NL3 interaction. For nonuniform nuclear matter we approximate the unit lattice as a spherical Wigner-Seitz cell, wherein the meson mean fields and nucleon Dirac wave functions are solved fully self-consistently. We also calculate uniform nuclear matter for a wide range of temperatures, densities, and proton fractions, and match them to non-uniform matter as the density decreases. The calculations took over 6,000 CPU days in Indiana University's supercomputer clusters. We tabulate the resulting EoS at over 107,000 grid points in the proton fraction range $Y_P$ = 0 to 0.56. For the temperature range $T$ = 0.16 to 15.8 MeV we cover the density range $n_B$ = 10$^{-4}$ to 1.6 fm$^{-3}$; and for the higher temperature range $T$ = 15.8 to 80 MeV we cover the larger density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$. In the future we plan to study low density, low temperature (T$<$15.8 MeV), nuclear matter using a Virial expansion, and we will match the low density and high density results to generate a complete EoS table for use in astrophysical simulations of supernova and neutron star mergers.

Precise simulations for future gravitational wave detectors

The emerging science of gravitational wave astronomy is optimistically named. Astronomy depends ultimately on observations, yet the only output of gravitational wave detectors has so far been noise generated within the instruments. There is good reason, based on experimental and theoretical progress, to believe that things are about to change. As an example of progress on the theoretical side, Kenta Kiuchi of Waseda University, Yuichiro Sekiguchi of the National Astronomical Observatory, Masaru Shibata of Kyoto University (all in Japan), and Keisuke Taniguchi of the University of Wisconsin, US, report in Physical Review Letters simulations of neutron star mergers that reveal new details of the gravitational waves they are expected to emit [1]. The effort to detect gravitational waves started humbly fifty years ago with Joe Weber’s bar detectors [2]. Today the field is a thriving example of Big Science, including large facilities [3] in the US (LIGO) and Italy (VIRGO), smaller installations in Germany (GEO 600) and Japan (TAMA, LCGT), and potential future detectors in Australia (AIGO) and India (INDIGO). LIGO, the best funded and so far the most sensitive of these instruments, is preparing a major upgrade called Advanced LIGO. In parallel with the development of ground-based detectors, there has been substantial design progress for detectors in space. The principal example is LISA [4], which received effusive endorsement from the National Academy of Sciences: “LISA is an extraordinarily original and technically bold mission concept. The first direct detection of low-frequency gravitational waves will be a momentous discovery, of the kind that wins Nobel Prizes” [5]. Space-based detectors will not likely be making that low-frequency (< 0.1 Hz) discovery for another ten years at least—not for lack of inherent sensitivity or progress in technology development, but rather because rapid deployment is not a characteristic of billion-dollar space research missions. Meantime, the effort to improve ground-based detectors, which operate at higher frequency (10 to 10, 000 Hz), is proceeding apace. What is the motivation compelling some of us to spend entire careers building telescopes that have yet to see the gravitational equivalent of first light? The thrall of zero is one conceivable answer. That is, the absence of signals at predicted levels places real constraints on astrophysical phenomena, and ultimately could test Einstein’s theory of general relativity. But most of us would trade a thick stack of publications with “search for” in the title for a single thin “discovery of.” It’s not about zero. Rather, the case that LIGO and VIRGO are almost good enough to see signals stands up to scrutiny. This is not simple optimism: the detection prediction is derived from a synthesis of electromagnetic astronomy and astrophysical models of sources that seem inevitable. For many years the favored source of gravitational waves for ground-based detectors has been the inspiral of a compact binary system consisting of one neutron star plus a companion that is either another neutron star or a black hole (Fig. 1, top). The orbital motion generates gravitational radiation at a frequency that chirps as the orbit decays and speeds up. The chirp waveform can be calculated accurately from a handful of parameters such as the masses and spins of the two stars and the inclination angle of the orbital plane. This waveform parameterization allows for coherent integration of the last minute or so of the life of the binary system, when the gravitational wave signal is strongest. In the 1987 proposal to the National Science Foundation that first described the LIGO concept [6], Kip Thorne had this to say about detection prospects in general: “The most certain of the sources is coalescence of neutron-star binaries: Estimates based on pulsar statistics in our own galaxy suggest that to see 3 such events

NEUTRINO SIGNATURES AND THE NEUTRINO-DRIVEN WIND IN BINARY NEUTRON STAR MERGERS

We present VULCAN/2D multigroup flux-limited-diffusion radiation-hydrodynamics simulations of binary neutron star mergers, using the Shen equation of state, covering ≳ 100 ms, and starting from azimuthal-averaged two-dimensional slices obtained from three-dimensional smooth-particle-hydrodynamics simulations of Rosswog & Price for 1.4M☉ (baryonic) neutron stars with no initial spins, co-rotating spins, or counter-rotating spins. Snapshots are post-processed at 10 ms intervals with a multiangle neutrino-transport solver. We find polar-enhanced neutrino luminosities, dominated by ¯νe and “νμ” neutrinos at the peak, although νe emission may be stronger at late times. We obtain typical peak neutrino energies for νe, ¯νe, and “νμ” of ∼12, ∼16, and ∼22 MeV, respectively. The supermassive neutron star (SMNS) formed from the merger has a cooling timescale of ≾ 1 s. Charge-current neutrino reactions lead to the formation of a thermally driven bipolar wind with (M·) ∼ 10^−3 M☉ s^−1 and baryon-loading in the polar regions, preventing any production of a γ-ray burst prior to black hole formation. The large budget of rotational free energy suggests that magneto-rotational effects could produce a much-greater polar mass loss. We estimate that ≾ 10^−4 M☉ of material with an electron fraction in the range 0.1–0.2 becomes unbound during this SMNS phase as a result of neutrino heating. We present a new formalism to compute the νi ¯νi annihilation rate based on moments of the neutrino-specific intensity computed with our multiangle solver. Cumulative annihilation rates, which decay as ∼t^−1.8, decrease over our 100 ms window from a few ×1050 to ∼ 1049 erg s−1, equivalent to a few ×10^54 to ∼10^53 e−e+ pairs per second.

Gravitational Waves from Relativistic Neutron-Star Mergers with Microphysical Equations of State

The gravitational wave (GW) emission from a set of relativistic neutron-star (NS) merger simulations is analyzed and characteristic signal features are identified. The distinct peak in the GW energy spectrum that is associated with the formation of a hypermassive merger remnant has a frequency that depends strongly on the properties of the nuclear equation of state (EOS) and on the total mass of the binary system, whereas the mass ratio and the NS spins have a weak influence. If the total mass can be determined from the inspiral chirp signal, the peak frequency of the post-merger signal is a sensitive indicator of the EOS.

Relativistic neutron star merger simulations with non-zero temperature equations of state

An extended set of binary neutron star (NS) merger simulations is performed with an approximative treatment of general relativity to systematically investigate the influence of the nuclear equation of state (EoS), the NS masses, and the NS spin states prior to merging. The general relativistic hydrodynamics simulations are based on a conformally flat approximation to the Einstein equations and a Smoothed Particle Hydrodynamics code for the gas treatment. We employ the two non-zero temperature EoSs of Shen et al. (1998a, Nucl. Phys. A, 637, 435; 1998b, Prog. Theor. Phys., 100, 1013) and Lattimer & Swesty (1991, Nucl. Phys. A, 535, 331), which represent a “harder” and a “softer” behavior, respectively, with characteristic differences in the incompressibility at supernuclear densities and in the maximum mass of nonrotating, cold neutron stars. In addition, we use the cold EoS of Akmal et al. (1998, Phys. Rev. C, 58, 1804) with a simple ideal-gas-like extension according to Shibata & Taniguchi (2006, Phys. Rev. D, 73, 064027), in order to compare with their results, and an ideal-gas EoS with parameters fitted to the supernuclear part of the Shen-EoS. We estimate the mass sitting in a dilute “torus” around the future black hole (BH) by requiring the specific angular momentum of the torus matter to be larger than the angular momentum of the ISCO around a Kerr BH with the mass and spin parameter of the compact central remnant. The dynamics and outcome of the models is found to depend strongly on the EoS and on the binary parameters. Larger torus masses are found for asymmetric systems (up to ~ for a mass ratio of 0.55), for large initial NSs, and for a NS spin state which corresponds to a larger total angular momentum. We find that the postmerger remnant collapses either immediately or after a short time when employing the soft EoS of Lattimer& Swesty, whereas no sign of post-merging collapse is found within tens of dynamical timescales for all other EoSs used. The typical temperatures in the torus are found to be about MeV depending on the strength of the shear motion at the collision interface between the NSs and thus depending on the initial NS spins. About of NS matter become gravitationally unbound during or right after the merging process. This matter consists of a hot/high-entropy component from the collision interface and (only in case of asymmetric systems) of a cool/low-entropy component from the spiral arm tips.

Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits

Two relations, the virial relation ${M}_{\mathrm{ADM}}{=M}_{\mathrm{K}}$ and the first law in the form $\ensuremath{\delta}{M}_{\mathrm{ADM}}=\ensuremath{\Omega}\ensuremath{\delta}J,$ should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, ${M}_{\mathrm{ADM}},$ ${M}_{\mathrm{K}},$ J, and $\ensuremath{\Omega}$ are the Arnowitt-Deser-Misner (ADM) mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $\ensuremath{\delta}$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between ${M}_{\mathrm{ADM}}$ and ${M}_{\mathrm{K}}$ and between $\ensuremath{\delta}{M}_{\mathrm{ADM}}$ and $\ensuremath{\Omega}\ensuremath{\delta}J$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

Coalescing neutron stars -A step towards physical models

In this paper we present a compilation of results from our most advanced neutron star merger simulations. Special aspects of these models were refered to in earlier publications (Ruffert & Janka [CITE]; Janka et al. [CITE]), but a description of the employed numerical procedures and a more complete overview over a large number of computed models are given here. The three-dimensional hydrodynamic simulations were done with a code based on the Piecewise Parabolic Method (PPM), which solves the discretized conservation laws for mass, momentum, energy and, in addition, for the electron lepton number in an Eulerian frame of reference. Up to five levels of nested cartesian grids ensure higher numerical resolution (about 0.6km) around the center of mass while the evolution is followed in a large computational volume (side length between 300 and 400km). The simulations are basically Newtonian, but gravitational-wave emission and the corresponding back-reaction on the hydrodynamic flow are taken into account. The use of a physical nuclear equation of state allows us to follow the thermodynamic history of the stellar medium and to compute the energy and lepton number loss due to the emission of neutrinos. The computed models differ concerning the neutron star masses and mass ratios, the neutron star spins, the numerical resolution expressed by the cell size of the finest grid and the number of grid levels, and the calculation of the temperature from the solution of the entropy equation instead of the energy equation. The models were evaluated for the corresponding gravitational-wave and neutrino emission and the mass loss which occurs during the dynamical phase of the merging. The results can serve for comparison with smoothed particle hydrodynamics (SPH) simulations. In addition, they define a reference point for future models with a better treatment of general relativity and with improvements of the complex input physics. Our simulations show that the details of the gravitational-wave emission are still sensitive to the numerical resolution, even in our highest-quality calculations. The amount of mass which can be ejected from neutron star mergers depends strongly on the angular momentum of the system. Our results do not support the initial conditions of temperature and proton-to-nucleon ratio needed according to recent work for producing a solar r-process pattern for nuclei around and above the peak. The improved models confirm our previous conclusion that gamma-ray bursts are not powered by neutrino emission during the dynamical phase of the merging of two neutron stars.